Answers
Answer:
a5 = 122
Explanation:
Given:
a1 = 2an = -3aₙ₋₁ + 2Solve:
a1 = 2
a2 = -3a1+2 = -3(2)+2 = -4
a3 = -3a2 + 2 = -3(-4)+2 = 14
a4 = -3a3 + 2 = -3(14) + 2 = -40
a5 = -3a4 + 2 = -3(-40) + 2 = 122
Answer:
a₅ = 122
Step-by-step explanation:
What is a₅ for the sequence defined by:
[tex]\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_{n-1}+2\\\end{array}\right\\\\\\\hrule[/tex]
Letting n=2:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{2-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{1}+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4[/tex]
Letting n=3:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{3-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{2}+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14[/tex]
Letting n=4:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{4-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{3}+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40[/tex]
Letting n=5:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{5-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{4}+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}[/tex]
Related Questions
Please help! Algebra 2
Answers
[tex]y = \sqrt[3]{x - 8} [/tex]
When translating the function in the positive x direction, we have to subtract the value from x
Convert from radians to degrees. Use pi = 3.14. Round your answer to the nearest tenth of a degree.
1.4 radians = _____
A. 80.3*
B. 25.7*
C. 40.1*
D. 15*
E. 131.8*
Need an answer STAT. Please :( I’ll give brainliest Fr
Answers
[tex]1.4 ~ \text{Radians}\\\\=\left( 1.4 \times \dfrac{180}{\pi}\right)^{\circ}\\\\=\left( \dfrac{252}{3.14}\right)^{\circ}\\\\=(80.3)^{\circ}[/tex]
[tex]\text{Hence the answer is A.}[/tex]
what's the value of X?
Answers
Answer:
x=55
Step-by-step explanation:
since it’s a right angle do 90*-35*=55*
Hope this helps! ;-)
if the average of 8 numbers is 12 what is the sum of 8 numbers
Answers
Answer:
Step-by-step explanation:
i do not feel like saying all the info soooo yea the answer is drumroll pls
16 i think well thats what i got
A marketing company is interested in the proportion of people that will buy a particular product. Match the vocabulary word with its corresponding example.
Answers
Each of the statistical jargons will be matched to the corresponding meaning or similarity or example.
Matching word to the corresponding example?The corresponding example of the word can be matched as follows:
Population : All the people in the marketing company region.
In statistics, a population is a group of individuals from which are subject to study.
Sample: The 380 randomly selected people who are observed to see if they will buy the product.
A sample represents the group of interest from a population, this group represent the data.
Variable: The answer Yes or No to whether a person bought the product Variable in statistic are any number or quantity that can be measured.
Data: The list of the 380 Yes or No answers to whether the person bought the product.
Data are the figures that are collected, analysed, and summarized for interpretation.
Parameter: The proportion of all people in the company's region who buy the product
Statistics: The proportion of the 380 observed people who buy the product
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What would the graph of f(x)=2arcsin (x-4)+1, look like?
Answers
The graph of the given function f(x)=2arcsin (x-4)+1, looks like the curve.
We have given that the function
f(x)=2 arcsin (x-4)+1,
We have to determine the graph of f(x)
Therefore we gave
Graph
Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
What are the coordinates of the graph?
An ordered pair (x, y) represents a position of a point on a coordinate graph, where x is the number on the x-axis that the point lines up with and y is the number on the y-axis that the point lines up with.
The numbers x and y in the ordered pair (x, y) are called coordinates.
We find the coordinate of the given graphs and draw a graph of the given function.
x f(x)
3 −π−1
7/2 −π/3−1
4 −1
9 2π/3−1
5 π−1
Therefore the graph of the given function is
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find the volume of this figure. round your answer to the nearest hundredth. if necessary
#8
Answers
Answer:
30 miles²
Step-by-step explanation:
To solve the area of the prism we have to multiply the area of the base * the height of the prism. The base of the prism is a right triangle.
(b*h)÷2 = Area of a triangle
Base = 4
Height = 3
Now:
(4*3)/2 = 6 miles²
Now we have to multiply 6 miles² by 5 as our height.
We get 30 miles² as the volume of the figure.
. Use the vectors v = -i +2j and w= -3i + 4j to find 5v + 8w.
O-29i+42j
O 10i-16j
O-4i + 7j
O2i+ 6j
Answers
put values
5(-i+2j)+8(-3i+4j)Do like you do algebraic addition
-5i+10j-24i+32j-5i-24i+10j+32j-29i+42jOption A
PLEASE HELP FOR BRAINLIEST :(((
Find the circumference and the area of a circle with radius 9m.
Use the value 3.14 for pi, and do not round your answers. Be sure to include the correct units in your answers.
Answers
The circumference and the area of a circle with a radius of 9m is 28.26
How to find the circumference
The circumference of a circle is its perimeter or distance around it. It is denoted by C in math formulas and has units of distance, such as millimeters (mm), centimeters (cm), meters (m), or inches (in). It is related to the radius, diameter, and pi using the following equations:
Given that:
Circumference of Circle = [tex]2\pi r[/tex]
[tex]9x=28.26[/tex]
[tex]9*3.14=28.26c[/tex]
[tex]or[/tex] [tex]28.26c[/tex] ÷ [tex]\pi(3.14)=9r[/tex]
Therefore, The circumference and the area of a circle with a radius of 9m is 28.26
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In a classroom of 20 kids, 3 girls are named Stephanie and 2 boys are
named John. The probability that a student picked at random is named
something other than Stephanie or John is what out of what?
Answers
Answer:
3/4 or 15/20
Step-by-step explanation:
this is because, you know there is 3 girls named the same thing and two boys named the same thing so if you know there are 20 people in the class, you do 3g + 2b = 5/20
So the fraction is either 15/20 or 3/4 for reduced fraction.
Other question! 5th grade! help asap
Answers
The names of this polygon include:
Acute triangle. Scalene triangle. Which polygon is described?The polygon given has three sides which means that it is a triangle. It is an acute triangle because the angles are all less than 90°.
It is also a scalene triangle because all the sides have different lengths from each other.
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Answer:
Step-by-step explanation:
I: acute triangle
L: Isosceles triange
(sorry if im wrong i have not done this in a good few years lol)
Help. Please and thanks.
Answers
Answer:
(2,6)
Step-by-step explanation:
What is a dilation?
A dilation is a type of transformation that resizes an object.
To apply a dilation ( find the coordinates of a point after a dilation ) you must multiply the x and y values of the coordinates by the scale factor
Applying the dilation rule
We want to find the coordinate of vertex B after a dilation with a scale factor of 2. To do so we multiply the x and y value of vertex b by the scale factor or 2
Current coordinates of the triangle :
A(1,1) B(1,3)C(3,1)Coordinates after dilation
A' = (1,1) ===> (1×2,1×2) ===> (2,2)
B' = (1,3) ===> (1×2,3×2) ===> (2,6)
C' = (3,1) ===> (3×2,1×2) ===> (6,2)
The coordinate of the vertex B after the dilation is (2,6)
A rectangular school yard is 96 meters wide and 178 meters long. What is its perimeter?
Answers
Answer: 69 square meters
Step-by-step explanation:
) Your 2 year investment of $5,300 earns 2.9% and is compounded annually. What will
your total return be?
Answers
The total amount of return will be 5611.8573. The principal amount is compounded annually.
What is compound interest?Compound interest is computed on a loan or deposit based on the starting principle and the preceding period's accrued interest.
The given data;
P(PRINCIPAL)=5300
r(rate)=2.9%
n=1
t(time)=2
The total amount of return is found as;
[tex]\rm A= 5300 (1+\frac{29}{100} )^2 \\\\ A=5611.8573[/tex]
Hence,the total amount of return will be 5611.8573.
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Assume that 48% of the voters in New York favor a certain legislative proposal. De- termine how many voters in New York need to be sampled so that the magnitude of the difference between the observed relative frequency of those favoring the proposal and the population frequency does not exceed 0.01 with probability 0.99.
Answers
The number of the voters in the Newyork need to be sampled will be P=19,782.
What is Probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
It is given in the question that:-
Voters percentage=48%
Margin of error=0.01
Z value at 0.99 = 2.58
By using the formula:-
[tex]\rm M=z\sqrt{\dfrac{\pi(1-\pi)}{n}[/tex]
By putting the values:-
[tex]0.01=2.58\sqrt{\dfrac{0.48(1-0.48)}{n}[/tex]
[tex]\sqrt{n}=\dfrac{1.40}{0.01}[/tex]
[tex]n=19784[/tex]
Hence the number of the voters in the Newyork need to be sampled will be P=19,782.
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helppppp find the value of a and b
Answers
Answer:
<a = <b = 60°
Step-by-step explanation:
<a and <b is vertically opposite of each other, thus equal each other. 90 - 30 = <b = <a.
Answer:
a and b are equal so a and b are 60°
Find the slope of the line that passes through the following two points. (1,0) and (3,0)
Answers
y = - 0
The line is horizontal.
in a certain triangle angle c is 40 degrees more than the sum of the measure of angle a and angle b. the measure of angle a is 20 degrees less than the measure of angle b. find the measure of each angle
Answers
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
angle c = angle a + angle b + 40
angle a = angle b - 20
angle a + angle b + angle c = 180
using the second equation in the first :
angle c = (angle b - 20) + angle b + 40 = 2×angle b + 20
using this and the second equation in the third equation :
(angle b - 20) + angle b + (2×angle b + 20) = 180
4×angle b = 180
angle b = 45°
angle a = angle b - 20 = 45 - 20 = 25°
angle c = angle a + angle b + 40 = 25 + 45 + 40 = 110°
How do i make a bestfriend
Answers
Answer:
Just add me and let's our journey begins :3
Step-by-step explanation:
Just add me and let's our journey begins :3
need help with this math
Answers
Answer:
h = 5 :)
Step-by-step explanation:
Nick has planted 20 flowers and can plant 7 flowers an hour, Rachel planted 5 flowers and can plant 10 flowers an hour.
f = 7h + 20
f = 10h + 5
f = 7(1) + 20 = 27
f = 10(1) + 5 = 15
(Not this one)
f = 7(2) + 20 = 34
f = 10(2) + 5 = 25
(nope..)
f = 7(3) + 20 = 41
f = 10(3) + 5 = 35
(nope!)
f = 7(4) + 20 = 48
f = 10(4) + 5 = 45
(close, but no)
f = 7(5) + 20 = 55
f = 10(5) + 5 = 55
(Yes!)
||||||
(Multiple Choice and Picture Attached) Will give Brainiest!!
Using the box-and-whisker plot shown, find the quartile values and
Q--8, Q, = 8
8
O
Q=-4, = 6
6
O
q=-4, = 8
8
--8,Q,- 4
Answers
Answer:
Q1 = -4, Q2 = 6
Step-by-step explanation:
In this box-and-whisker plot, the first vertical line is the first quartile (-4), the second vertical line is the median (4), and the vertical line is the third quartile (6). The box contains the middle 50% of the data set.
write 28% as a fraction
Answers
Answer:
28% as a fraction can be written in many ways. The most simplest way to convert a percentage to a fraction would just to put it over 100. For example, 50% would be 50/100 therefore 28% would be 28/100.
However, we can simplify that fraction even more by doing (28/4)/(100/4) which would give us 7/25.
Hope this helps!
In "The Emperor's New Clothes" what does the opening tell you about the narrator?
A. second person narrator
B. third person narrator
C. no narrator
Answers
Answer:
third person
Step-by-step explanation:
1. From where do we get fibre?
Answers
Answer:
Grain, fruit, and vegetables are where natural fibers are found.
write the equation of the line passing through the point (-4 "-7)" and (8 "-17)"
Answers
Answer:
[tex]y = -\dfrac{5}{6} x -\dfrac{31}{3}[/tex]
In order to find equation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{rise}{run}[/tex]
[tex]\rightarrow \sf slope: \dfrac{-17-(-7)}{8-(-4)}[/tex]
[tex]\rightarrow \sf slope: -\dfrac{5}{6}[/tex]
Then find equation using:
y - y1 = m(x -x1) where (x1, y1) are points, m is slope
[tex]\sf \rightarrow y - (-17) = -\dfrac{5}{6} (x - 8)[/tex]
[tex]\sf \rightarrow y = -\dfrac{5}{6} x + \dfrac{20}{3} -17[/tex]
[tex]\sf \rightarrow y = -\dfrac{5}{6} x -\dfrac{31}{3}[/tex]
Whát are the quotient and remainder of (x^5-x^3 +1-5) / (x - 2)?
a. x + 2x2 + 9x + 13; 21
x + 2x2 + 3x + 6x + 13; -21
b. x + 2x + 3x2 + 6x + 13; 12
d. + 2x2 + 3x2 + 6x + 13:21
Answers
Answer:
x⁴+2x³ +3x²+6x +12r is the answer
25 points please help
Answers
Answer:
See below ~
Step-by-step explanation:
The functions which have a range ≥ -1 :
y = |x - 1| + 2y = |x + 2| - 1The first function (according to the attachment) is not part of this because on applying any value for x, it will be either less than or equal to -1.
Tyler simplified the expression x³y9. His procedure is shown below.
1
31/1
³y-9
What is Tyler's error?
Both powers should be in the numerator with positive exponents.
Both powers should be in the denominator with positive exponents.
The power
The power
should be in the numerator and the power y9 in the denominator.
should be in the numerator and the power x3 in the denominator.
Answers
Answer:
(b) both powers should be in the denominator with positive exponents
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
The correct simplification is ...
[tex]x^{-3}y^{-9}=\dfrac{1}{x^3}\cdot\dfrac{1}{y^9}=\boxed{\dfrac{1}{x^3y^9}}[/tex]
Both variables should have positive exponents in the denominator.
Complete the table to show the area of each circle.
Answers
Answer: look at my work its 10 pi cm ^2
Step-by-step explanation:
Answer:
Below in bold.
Step-by-step explanation:
Area of:
The large circle = π r^2 = π * 10^2 = 100π
The small circle = π * 5^2 = 25π.
help me please i don't know what to do
Answers
Answer:
a. a = 1, b = -5, c = -14
b. a = 1, b = -6, c = 9
c. a = -1, b = -1, c = -3
d. a = 1, b = 0, c = -1
e. a = 1, b = 0, c = -3
Step-by-step explanation:
a. x-ints at 7 and -2
this means that our quadratic equation must factor to:
[tex](x-7)(x+2) = 0[/tex]
FOIL:
[tex]x^2 + 2x - 7x - 14 = 0[/tex]
Simplify:
[tex]x^2 - 5x - 14 = 0[/tex]
a = 1, b = -5, c = -14
b. one x-int at 3
this means that the equation will factor to:
[tex](x-3)^2=0[/tex]
FOIL:
[tex]x^2 - 3x - 3x +9 = 0[/tex]
Simplify:
[tex]x^2 - 6x + 9 = 0[/tex]
a = 1, b = -6, c = 9
c. no x-int and negative y must be less than 0
This means that our vertex must be below the x-axis and our parabola must point down
There are many equations for this, but one could be:
[tex]-x^2-x-3=0[/tex]
a = -1, b = -1, c = -3
d. one positive x-int, one negative x-int
We can use any x-intercepts, so let's just use -1 and 1
The equation will factor to:
[tex](x+1)(x-1)=0[/tex]
This is a perfect square
FOIL:
[tex]x^2-1=0[/tex]
a = 1, b = 0, c = -1
e. x-int at [tex]\sqrt{3} , -\sqrt{3}[/tex]
our equation will factor to:
[tex](x+\sqrt{3} )(x-\sqrt{3)} =0[/tex]
This is also a perfect square
FOIL and you will get:
[tex]x^2 - 3 = 0[/tex]
a = 1, b = 0, c = -3
